List questions from cauchy-schwarz-inequality

Published on 16 May 2026 - 18:51

93

Views

Prove that $\frac{x^{2}}{(x-y)^{2}}+\frac{y^{2}}{(y-z)^{2}}+\frac{z^{2}}{(z-x)^{2}} \geq 1$

Published on 28 Mar 2026 - 7:15

68

Views

Is there any constant $c$ satisfying the inequality

Published on 10 Apr 2026 - 8:17

160

Views

If $x+y+z=1$ Find the maximum of $\frac{x-y}{\sqrt{x+y}}+\frac{y-z}{\sqrt{y+z}}+\frac{z-x}{\sqrt{z+x}}$

Published on 14 Apr 2026 - 18:56

115

Views

Does this 2-norm inequality hold?

Published on 08 Apr 2026 - 16:22

138

Views

How can I approach this inequality?

Published on 11 May 2026 - 5:01

821

Views

Using Cauchy-Schwarz to prove the triangle inequality

Published on 14 Apr 2026 - 12:14

151

Views

Prove that $\sqrt{\frac{2 a^{2}+b c}{a^{2}+2 b c}}+\sqrt{\frac{2 b^{2}+c a}{b^{2}+2 c a}}+\sqrt{\frac{2 c^{2}+a b}{c^{2}+2 a b}} \geq 2 \sqrt{2}$

Published on 28 Mar 2026 - 7:15

134

Views

If $x+y+z=1$ prove $ \sqrt{x+\frac{(y-z)^{2}}{12}}+\sqrt{y+\frac{(z-x)^{2}}{12}}+\sqrt{z+\frac{(x-y)^{2}}{12}} \leq \sqrt{3} $

Published on 25 Mar 2026 - 19:07

188

Views

If $a+b+c+d=4$ Prove that $ \sqrt{\frac{a+1}{a b+1}}+\sqrt{\frac{b+1}{b c+1}}+\sqrt{\frac{c+1}{c d+1}}+\sqrt{\frac{d+1}{d a+1}} \geq 4 $

Published on 11 May 2026 - 6:44

154

Views

Prove that $\frac{1}{1 - \sqrt{ab}} + \frac{1}{1 - \sqrt{bc}} + \frac{1}{1 - \sqrt{ca}} \leq \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$

Published on 28 Mar 2026 - 7:15

114

Views

Olympiad Inequality: Cauchy Schwartz

Published on 11 May 2026 - 7:40

179

Views

Application of Cauchy-Schwarz to sum of expected values

Published on 11 Apr 2026 - 20:27

196

Views

Maximize $a^T x$ with constraint on $2$-norm of $x$

Published on 11 May 2026 - 10:38

40

Views

Inequality Integral who involves logarithms and exponentials

Published on 14 May 2026 - 23:21

List Question

Stuck when transforming and solving this

Prove that $\frac{x^{2}}{(x-y)^{2}}+\frac{y^{2}}{(y-z)^{2}}+\frac{z^{2}}{(z-x)^{2}} \geq 1$

Is there any constant $c$ satisfying the inequality

If $x+y+z=1$ Find the maximum of $\frac{x-y}{\sqrt{x+y}}+\frac{y-z}{\sqrt{y+z}}+\frac{z-x}{\sqrt{z+x}}$

Does this 2-norm inequality hold?

How can I approach this inequality?

Using Cauchy-Schwarz to prove the triangle inequality

Prove that $\sqrt{\frac{2 a^{2}+b c}{a^{2}+2 b c}}+\sqrt{\frac{2 b^{2}+c a}{b^{2}+2 c a}}+\sqrt{\frac{2 c^{2}+a b}{c^{2}+2 a b}} \geq 2 \sqrt{2}$

If $x+y+z=1$ prove $ \sqrt{x+\frac{(y-z)^{2}}{12}}+\sqrt{y+\frac{(z-x)^{2}}{12}}+\sqrt{z+\frac{(x-y)^{2}}{12}} \leq \sqrt{3} $

If $a+b+c+d=4$ Prove that $ \sqrt{\frac{a+1}{a b+1}}+\sqrt{\frac{b+1}{b c+1}}+\sqrt{\frac{c+1}{c d+1}}+\sqrt{\frac{d+1}{d a+1}} \geq 4 $

Prove that $\frac{1}{1 - \sqrt{ab}} + \frac{1}{1 - \sqrt{bc}} + \frac{1}{1 - \sqrt{ca}} \leq \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$

Olympiad Inequality: Cauchy Schwartz

Application of Cauchy-Schwarz to sum of expected values

Maximize $a^T x$ with constraint on $2$-norm of $x$

Inequality Integral who involves logarithms and exponentials

Trending Questions

Popular # Hahtags

Popular Questions